Intuition Amplifiers: Science behind Stealth Trader

Dr. Alex Bogdan

Table of Contents

1. Introduction
2. Perception
3. Sentiment
4. Dissecting the Order Book
5. Perceptual Dynamics
6. Sliding Time Windows
7. Discrete Time Filters
8. Splines
9. Spline Spectrums
10. Building the Intuition Amplifiers
11. Stealth Sentiment Spectrum Gauge
12. Use of Colors
13. Traders’ Commitment Gauge
14. Trading Equilibrium Gauge
15. Conclusion

1. Introduction

Mathematical Psychology is, unfortunately, not a very well-known branch of Artificial Intelligence. It represents an approach to psychological research based on mathematical modeling of perceptual, cognitive, and motor processes of humans as individuals and their collectives. Mathematical Psychology objectives include establishing logical rules and associative patterns that relate quantifiable stimulus characteristics with quantifiable behavior.

One of the main fields of research in Mathematical Psychology is stimulus detection theory. This field is dedicated to developing tools to quantify the ability to discern between meaningful, information-rich patterns (called stimuli in humans and signals in machines) and random patterns that mask useful information (called noise, consisting of background stimuli and random activity of the detection mechanism). In both machines and human operators, pattern detection abilities significantly depend on how well the detection mechanisms can “filter” the noise and “enhance” the useful informational patterns.

For creating tools that can enhance (amplify) the abilities of stimuli detection, Mathematical Psychologists often focus on how a detecting system will process a signal, and where its threshold levels will be. Once a signal detection model can explain how changing the threshold will affect the ability to discern the stimuli, it can be effectively used to create various methods of enhancing the stimuli detection process in both the operator and the machine.

When the detecting system, however, is a human being, experience, anticipation, intuition, expectations, physiological state, and other factors can affect the efficiency and accuracy of the stimuli detection process. For instance, a blind man can easily detect many of the sound patterns that normally are not sensed by an average person. By efficiently detecting and recognizing those subtle sounds, a blind person could create a fairly accurate perception of his/her environment even without using visual receptors.

By studying how our perception is formed, Mathematical Psychology offers a unique approach to creating many practical tools. Additionally, it provides formal methods for systematically enhancing such “illusive” human abilities as intuition, anticipation, skill development, and associative pattern recognition.

It has been conclusively proven that in many areas of human activities, logical (linear) decision-making is insufficient to deal with the dynamics of rapidly changing environmental conditions. When we drive a car, fly a plane, or trade markets, our ability to succeed strictly depends on how fast and accurately we make crucial decisions. Highly dynamic, rapidly evolving situations (especially if they are surrounded by a high degree of uncertainty) demand us to be nimble and not to rely on the time-consuming and sometimes misleading “If – Then” type of decision-making logic. Skills, intuition, experience, anticipation, and reflexes, as well as emotions and feelings, help us cope with those situations when our very survival depends on split-millisecond decisions.

The rapid development of computers in the past 30 to 40 years has lured us into thinking that they are the solution to any problem and the answer to the challenges we face. Indeed, computers can outperform us in virtually any activity that involves number crunching, data storage, search, and sorting. However, there are areas of intellectual activities that seem to be out of reach for even the most powerful modern computers. In 2000, a group of scientists at Carnegie Mellon University developed a “Completely Automated Public Turing test to tell Computers and Humans Apart” – CAPTCHA. These types of tests were designed to be easy for a computer to generate but difficult for a computer to solve. For example, in the picture below, anyone could easily recognize the word as displayed; however, it would present a tremendous challenge for a computer to recognize this image and match it with the word “Computer”.

CAPTCHA is the most common proof of the vivid differences between computer algorithms and the associative pattern recognition abilities of humans.

There are, of course, numerous examples of explicit and vivid differences between humans and computers. An average human would experience tremendous difficulties when trying to multiply 2,345,321,098,213,469 by 323,425,580,982 just using his/her mental calculating abilities, and of course, modern computers can calculate the answer almost immediately. However, humans can easily tell when another person is in a “bad mood” by instantly reading that person’s very subtle facial expressions or body language. On the other hand, distinguishing between happy and angry expressions on your face would probably create an overwhelming challenge to even the most sophisticated computers. It is interesting that the very reason why humans have established such a great bond with dogs is because dogs, unlike the majority of other animals, have developed the ability to recognize human facial expressions and react to them accordingly. They are indeed “man’s best friend,” as the saying goes.

As a Mathematical Psychologist, I have been studying perceptual patterns observed in organized financial and commodities markets over the past 18 years. Like a starry night sky presents endless wealth of data to an astronomer, markets are the ultimate source of behavioral patterns, psychological observations, and perceptual anomalies for a Mathematical Psychologist. In this paper, I will present some of my findings that have ultimately led our company, QuantGate Systems, Inc., to create devices and software such as Stealth Trader, Market Sentiment Navigator, RTN Stealth, Perception Envelope Indicators, and many other perception-enhancing tools that we simply call “Intuition Amplifiers”.

2. Perception

Perception is a way to create the awareness or apprehension of things. It has long been a fascinating subject of research for psychologists and philosophers alike. The most common tool used in such research is the “perceptual illusion” – a way to create an object, a situation, or a visual image that perceptually appears other than it really is.

In the picture above, it appears that the letter “A” has two different shades of grey. In reality, the entire letter is painted with exactly the same color.

Endless numbers of very clever examples of how one could deceivingly create a wrong perception have been discussed in literature since the very early days of our civilization. Both the Old and New Testament, for example, contain many examples where different biblical figures used various forms of deception to create an illusion or a false perception in others to gain some sort of advantage. Wars were won, trillions of dollars were gained and lost, and millions of people have died or become famous simply because of the difference between the mass-created perception and the objective reality. We all know that there are no fundamental or objective reasons why the price of gold should almost triple since 2008 and why the price of tulip bulbs in 1637 had increased 40 times and then crashed back to almost zero in a short period of time. Those incredible price fluctuations are the results of drastic changes in the perceived value of goods that are bought and sold in the open markets. As a matter of fact, it is virtually impossible to calculate an objective value of anything that is not a necessity for our biological existence. Most of the things around us are valued strictly from the perception standpoint, where their desirability is significantly influenced by our senses of fashion, prestige, pride, etc.

The notions of nostalgic or sentimental values are well known to collectors of all sorts. An old mechanical watch that is by far less superior than modern electronic watches in terms of its main purpose (keeping accurate time) could have a value of a million dollars if that watch used to belong to a significant historical figure. Our emotions and feelings such as fear, greed, nostalgia, love, etc., are the main reasons behind the drastic changes in our perception and the way we value things around us. It also appears that we are not very capable of developing our own perceptions without communicating with each other and sharing our beliefs and feelings. Indeed, our own perceived values of things almost entirely depend on how we believe others would value them. If we believe that others may value gold higher in the future, we buy gold because we believe it costs less today than it will in a few months.

We all learned in school that the price of goods is a function of their supply/demand ratio. However, most of us don’t realize that both supply and demand are pretty much governed by our perception as well. Subjective desirability of things could dramatically increase our demand for them and, at the same time, create incredibly powerful incentives to resell, manufacture, find, or even obtain them by force (war or political dictatorship), thus increasing their supply.

From the very dawn of our civilization, we formed mechanisms to discover the perceived values of goods. Those mechanisms have evolved over the past few millennia but at their heart, they still have one of our most ancient activities – barter or trade. Trading usually involves an exchange of goods or services as well as an exchange of goods or services for money – a mutually accepted symbolic representation of value. Trading also involves the transfer of the ownership of goods and services from one person or entity to another. As a result of this exchange, the perceived value of goods or services is established and accepted by the majority of trading participants and could be used to determine their price today and how this price might change in the future. The same applies to the process of determining the price of any security or financial instrument.

A few hundred years ago, an incredibly efficient and powerful mechanism to formalize the trading process – The Securities Exchange (Exchange) was established, regulated, and socially accepted. It is considered by many to be the most ingenious and efficient vehicle ever invented in terms of its ability to discover the current perceived value of goods, securities, and financial instruments.

In the early 17th century, Amsterdam became the main trade center of the world. The Dutch East India Company (Dutch: Vereenigde Oost-Indische Compagnie, VOC, "United East India Company") was the main catalyst for the creation of an organized system of price discovery. This company became the first in the world to attract the capital needed for further expansion by issuing public shares at the beginning of 1602. The trade in VOC shares took place in a specially designed building that was open for trading in 1611. It marked the birth of the very first Stock Exchange in the world. Today, Exchanges continue to play a very significant role in our society and provide us with many tools to run our economy efficiently.

An Order Book of any Exchange is the list of orders (submitted either manually or electronically) that is used to record the interest of buyers and sellers in a particular financial instrument or product. Each Order Book is also associated with a trade or match engine that uses the information contained within to determine which orders can be filled, i.e., what trades can be made. A typical Order Book contains the list of interested buyers and sellers along with their identifiers, number of shares or contracts, and the prices that the buyers or the sellers are asking/bidding for the particular security. This list is usually sorted by the price levels, meaning that if, say, a bid comes at a certain price level, then all the offers listed at the same price level could be used to fill that bid. The highest bid and the lowest ask are referred to as the top of the book. They are interesting because they identify the potential price level for the very next trade. The price difference between the best or highest bid and the best or lowest ask is called the bid-ask spread.

It has been established that the two main manifestations of our perception are Action and Intent. Naturally, the only way for us to form an opinion about someone else’s perception is to observe his or her actions and assess their explicit exhibited intents. The Order Book is the only real-time window into the integrated perceptions of all the people who are currently involved in buying or selling a particular security. Indeed, the Order Book registers the intents of many market participants in the form of their Buy and Sell orders, and it has all the information about traders’ actions such as placing new orders, changing the price or size of their orders, moving existing orders closer or further away from the top of the book, canceling, and replacing them with new ones. All of these Order Book activities represent a wealth of information that could be used to quantify the integrated (collective) perception of traders known as “Traders’ Sentiment”.

3. Sentiment

Sentiment is a state of mind of an individual or a group of people that is a result of their perceptions, feelings, and emotions. It directly influences our attitude toward something and promotes our opinions, actions, and intents. Sentiment is responsible for the formation of our BIAS and it also underpins our Decision Making process. Sentiment manifests itself through the optimism or pessimism in financial markets, politics, and our social lives. An ability to quantify, assess, or measure sentiment enables us to anticipate or even predict future actions and intent, thus helping us to make decisions and guide our own actions accordingly.

There have been many attempts to quantify the sentiment of traders. A ratio between the open interests of Puts and Calls is just one example of using quantitative data to measure traders’ sentiment. Another is the “Commitments of Traders” report issued by the CFTC (Commodities Trading Commission), which shows a breakdown of each Tuesday’s open interest in markets where at least 20 traders hold open positions equal to or above the commission’s specific reporting levels it has established. Of course, creating a unit to objectively measure the sentiment and building the sentiment measuring scale are not easy tasks. As with many subjects studied in Mathematical Psychology, sentiment is a multidimensional phenomenon that is extremely difficult to model. However, if we narrow down the scope of actions that we are trying to anticipate, it creates the opportunity of quantifying the sentiment through those actions. This approach allows us to build indirect measurement scales to quantify the sentiment through the use of measuring units related only to those chosen actions. For example, if we only focus on buying and selling activities of traders, their sentiment could be described as “bullish” or “bearish,” thus creating the opportunity of quantifying it through the intensity of those actions. Overall, measuring the dynamics of the Order Book has been my approach to quantify traders’ sentiment. In turn, a quantified level of registered “Bullish” or “Bearish” sentiment is one of the most powerful tools for developing a reliable anticipation of upcoming price moves.

4. Dissecting the Order Book

Generally speaking, the Order Book is a mirror that reflects the intensity of Buying/Selling activities that, in turn, result in price fluctuations. By simply observing the ever-changing dynamics of the Order Book, one could literally “see” the “built-up pressure” on either the Bid or the Ask side of the book. It is also very apparent that this pressure eventually moves the top of the book towards the higher or lower price levels. If we could easily absorb all the significant changes of the Order Book in real-time, we could reliably anticipate immediate price changes for a security.

In the past, there was a special breed of traders who called themselves “tape readers.” The term gets its name from the old method of displaying trade, bid, and ask information on paper printed by ticker tape machines. Those traders could anticipate price fluctuations by simply watching the ticker tape that carried real-time prints of each trade, bid, and ask prices. As the speed of trading and trading frequency increased, there were fewer and fewer “tape readers”; it became much more difficult to reliably anticipate the price moves by just visually scanning the ticker tape. Today, there are very few “tape readers” left simply because the electronic equivalent of the old “tape” moves too fast for the human cortex to absorb and process it.

In the late 90s, electronic communication networks (ECNs) and other global electronic markets started to play a much more significant role in facilitating the trading of financial products outside of traditional stock exchanges. Island, Archipelago, GLOBEX, ECBOT are just a few names of electronic market pioneers. These electronic Exchanges have changed the very fabric of the trading process forever. The electronic version of the Order Book became available to traders from all walks of life. Different names such as Level II, Depth of the Market, Electronic Book, etc., are used by different exchanges and ECNs to refer to this tool to provide much greater transparency to the process of price discovery. Although most of those tools could only provide a partial look into the full Order Book (many Exchanges and data Providers only allow between 5 to 20 price levels of the book to be visible), they have created a unique ability to assess intensity, speed, liquidity, and general trader interest in Buying or Selling of a particular security. Some very talented traders have learned how to visually “read” the Order Book and have developed a unique skill set and ability to anticipate upcoming price moves, form their opinion about the general direction of the market (Market Sentiment or BIAS), and act on them. My colleagues and I have spent many hours observing those very talented and unique “book readers”. It was literally shocking and amazing to see one particular trader’s incredible abilities and phenomenal intuition that allowed him to spot brewing profit opportunities just by watching the Order Book of the COMEX Gold Futures contract. (Thank you, Simon, for sharing your incredible talent with me!)

Many traders would absolutely love to develop those skills. Unfortunately, for the overwhelming majority of us, the ability to visually “read the book” is not obtainable. In the next paragraph, I will try to explain why, but for now, I would just say that all of us, “non-book readers,” definitely need some sort of edge or “special glasses” to see what only 0.1% of all the traders in the world can see – Real Time Sentiment of Traders and their Intents imprinted within dynamic Order Books. Like an astronomer needs his powerful telescope to gaze at the darkest corners of our universe, we need something to enable us to see virtually “invisible” patterns of the Order Book. We need some equivalent of “market night goggles” - we need “Intuition Amplifiers”.

5. Perceptual Dynamics

Imagine that you are standing on top of a high-rise building, and below you is a busy street intersection with constant flows of cars in four different directions. Even if you had no idea about the intersection’s traffic rules, after observing its busy life for a while, you’d notice that if a car had a blinking light, it needs to turn left or right while giving way to cars that are moving straight through the intersection. You would also notice that when the cars are turning right, they will stop to let pedestrians cross the street. Soon, you could predict what should happen next when you spot a situation that you either witnessed before or now possess an understanding of and the logic of the traffic rules that govern the patterns.

Imagine now that you had a video recorder and filmed this intersection for five straight hours without thinking or noticing any patterns or rules about the movement of cars. You were just filming, and your main concern was to make sure that you document well everything that happened during these five hours. After you were done, you came home and watched this video. However, for whatever reason, your playback function started to play your recorded footage 1,000 times faster than it should have. Looking at the screen, you would not be able to make heads or tails of what was occurring. The movement of cars would resemble to you a chaotic movement of bees hovering around their beehive. The traffic rules would become virtually indiscernible, and no matter how long you would watch this video, you would not be able to understand what was going on and how to predict or even anticipate what might happen in the very next second. The cars on your screen would be moving too fast to leave you any hope of comprehending their mutual behavior. As a result, you would have no choice but to consider the logic of the intersection as unpredictable and the car movements utterly random.

The next day, you decided to fix your recorder and brought it to your neighborhood camera repair shop. You picked up your camera the day after and tried to watch the intersection video again. However, this time your recorder played back your video 1,000 times slower than it should have. All you would see now is a virtually static picture with the cars moving so slowly that it wouldn’t make any sense to you. Even if you would watch this video in its entire length (spending 5000 hours to watch it), you would forget what had happened a while back and you would again consider the logic as unpredictable and the car movements very slow and random.

The result of this mental experiment is quite obvious. We, as humans, can form our opinions and comprehend our environment only if the processes we observe have a very specific and, frankly, quite narrow dynamic range. In order to use our natural, genetically inherited abilities to understand logic, recognize patterns, develop associations, and comprehend situations, the processes we observe must be in a dynamic range that suits us best individually. Experimenting with this concept for several years (a subject for another white paper that is on my “to-do” list), I have discovered that the best dynamic ranges for different people vary rather significantly. The reason why the Great One - Wayne Gretzky could “see” split-millisecond scoring opportunities was that only he among all the players on the ice could process the development of game situations in such a highly dynamic range. That is why my dear friend Simon can “clearly see” the patterns in the Order Book that most of us cannot.

It appears that in order for us to comprehend highly dynamic or incredibly slow-developing situations, we must have a device that could “tune” the time scale of the observed reality to match the most suitable for our individual perception dynamic range. These devices should play the role of a slow-motion video of a bullet hitting an apple that would enable us to “see” the precise motion and impact of the bullet. Those devices in our world are called “Time Modulators,” and they are an essential part of every Intuition Amplifier we have built.

6. Sliding Time Windows

While writing this paper, the temperature outside of my office window suddenly dropped to 30 ºF. “That’s pretty cold,” I thought to myself, “I hope it is not an indication of a chilly summer that we have in Toronto once in a while”. It is the beginning of May, and the normal day temperature for this time of the year should be around 60 ºF. However, it is not the entire reason why I thought it was cold outside. I barely remember what kind of weather we had at this time a year ago. If it wasn’t for Google or Weather.com, I wouldn’t even know what the average temperature is at this time of the year. The reason I have noticed this sudden drop is because we just had a few very warm days with glorious sunshine and temperatures over 70ºF (also not very normal temperatures for the beginning of May). I vividly remember people wearing shorts and T-shirts just a few days ago, and now my neighbor’s kids were playing in their backyards wearing hats and warm coats. It appears that more recent events have a far greater influence on our perception than the events that happened a while ago. As the events move further into the past, their significance and impact on the future and the present diminishes exponentially (the actual formula to describe this phenomenon is part of our work but reserved for other papers with greater mathematical underpinnings in their content). Our memory naturally limits the time window of “relevance” to a few days or to a few years, depending on the actual significance of the observed events. Talking recently to a few Fund Managers about the events of the October 2008 market crash, I have noticed that they talk about it as this crash happened on another planet. They joked about it and described those events as something “interesting” but not having any influence on today’s decisions to load their portfolios with un-hedged Long positions (I bet that on October 10th, 2008, they did not take the situation that lightly). At the same time, the very recent and fairly modest sell-off on April 10th, 2012 made many investment managers worry about their exposure to Europe more so than the fact that exactly three years ago we scrapped the market’s bottom, and the S&P 500 index printed the infamous 666 (the “devil’s number”) price level.

Another example of the events’ relevant timing could be found when we observe the actions of Day Traders. These market participants couldn’t care less about what happened a week or even a few days ago. Their decisions are only influenced by very recent news and price actions. In general, any meaningful decision-making process requires a very specific time window to cover all the past significantly relevant events. This time window appears to be directly proportional to the time window of future Intents and Actions. We call this window the “Depth of Perception”.

As the present time of our decisions moves toward the future (leaving behind all the current events), the time window of relevance is moving as well. This Sliding Time Window always ends in the present and starts at a certain time interval back in the past. As this window slides towards the future, it only contains the most recent events and excludes the events that happened too far in the past.

Let us assume that we measure the significance of every event contained in the Relevant Events Sliding Time Window using the same scale. For example, if we look back at the last month’s weather conditions, we could rate each day of that month by the lowest and highest temperatures registered during the day. Comparing all the days, we can always find the highest and the lowest temperatures registered in the time interval covered by the Sliding Time Window. These temperatures play a very important role – they create the reference points for us to assess the current weather conditions. This scale will constantly evolve because it will always be based on a set of different events; some of them would disappear in the past, and some would get added as the Sliding Time Window moves towards the future. Even if the temperatures were not changing at all during the past couple of days, our perception of the current weather would change simply because every day we would use a different reference scale to assess the temperature.

This is a very powerful concept to consider. It enables us to “extract” normally hidden information that forms our perception. It could be used in many ways. Below, for example, is an illustration of this concept that uses the S&P 500 Index daily bar chart.

In this example, the current relative price levels to the Highest and Lowest prices of the 30-day Sliding Time Window would change not only when the current price changes but also when the new bars were included in the Sliding Time Window. Imagine that a new bar is added to the right of the chart above, and the bar at the beginning of the Sliding Time Window is removed from it as this window moves one time bar towards the future. This shift significantly impacts the relationship between the current price and the extreme levels of the Sliding Time Window. Indeed, as you can see above, the current price did not change much during the new bar interval (bar 31); however, the Dynamic Price Scale of the new 30-day window has changed significantly (the lowest price is now at the higher level, bar 2 instead of bar 1). This in turn drastically changes the relationship between the current price and the newly formed Dynamic Price Scale. As a result, our perception of the current price level changes as well.

If we calculate the percentage-based ratio between the current value (price, temperature, speed of a moving car, etc.) and the highest/lowest values of the Dynamic Scale, we would arrive at a normalized expression that varies between 0 and 100. This technique paves the way for efficient visualization of this very important component of the perception assessment process. It creates an extremely valuable tool for building Intuition Amplifiers.

7. Discrete Time Filters

Many of the processes around us are usually of an analog nature: the air temperature in certain geographic areas, the rate of fluid flow through a pipe, the buying or selling “pressure” of the Order Book, etc. To extract useful information about those processes using computers, we must first “digitize” those processes using Analog-to-Digital Converters (A/D Converters). A/D converters simply “sample” the values of the analog process every so often and present those values as a sequence of numbers. The process of sampling, by necessity, causes a loss of information. Indeed, if we are only sampling at particular times, for instance, all the information between those times is lost. However, if a useful signal is “polluted” with noise, this “loss” of information might be very useful. Digitization of analog signals often reduces the high-frequency noise of those signals, thus helping us to “see” useful patterns embedded in those signals a lot more clearly.

In finance, the digitizing process of price fluctuations is done on many levels. It starts with registering the price changes only when a price moves by a minimum allowed increment (minimum tick value). The price is usually then plotted as a bar chart where all the changes that occurred within one bar (a single time interval) are assumed to happen at the same time (usually at the end of the bar time interval). These bars could be formed using time intervals (time bar series), a fixed number of transactions (tick bars), fixed volume (volume bars), or fixed changes in price (quantum charts). All of these methods have the same purpose - to create a “cleaner” picture of market’s activities and compress information to enable better visualization of those activities. By comparing multiple time price charts of different bar intervals, one can draw a better conclusion of overall price behavioral patterns such as “trends”, “channels”, “breakouts,” etc. Obviously, the more time frames considered as inputs, the greater the chances of spotting some stable, reoccurring price patterns that might present a profit opportunity. However, an attempt to visually assess more than a few different time frames quickly saturates our mental abilities and results in the loss of perception. In other words, it is highly desirable to analyze as many time frames as possible, but “overloading” our visual cortex is highly unadvisable. The only solution to this problem is to reduce the number of time frames that we need to analyze without any significant loss of useful information and at the same time to increase our ability to visually process a much greater number of time frames.

Let us use time-based price bar charts to shed some light on the challenges mentioned above and specifically the S&P 500 index price charts again. If we create a chart with 5-minute bar intervals and at the same time we plot a 6-minute bar chart right beside it, we could easily see that those two charts are strongly correlated (they look virtually the same).

In other words, if we were trying to draw some conclusions using the 5-minute chart, we wouldn’t benefit much from adding the 6-minute chart into our analysis. If we are separately analyzing two situations that are highly correlated, we are wasting our resources; we might as well just focus on one of them. On another hand, the situation is very different if we look at the 5-minute chart and the 30-minute chart that have the same number of bars. Those charts look very different. The “bigger” picture provided by the 30-minute chart changes dramatically our perception of the S&P 500 index price behavior. We, for example, are not so sure anymore about the “trending” characteristics of the S&P 500 market that we definitely sensed by just looking at the 5-minute chart alone. Generally speaking, the less correlation there is between the processes we observe, the more variety we add to our decision-making process.

It is worth noticing that in the two cases above, we used very similar resources (we analyzed two charts in both cases), but we have dramatically improved our chances of developing much stronger anticipation by focusing on uncorrelated charts.

The principle of uncorrelated time frames and the methods of finding them were at the core of our development of different Intuition Amplifiers. This principle could also be efficiently used when processing the Sentiment information imprinted in the Order Book. We will discuss the application methods of this principle later in this paper.

8. Splines

Splines are types of curves, originally developed for ship-building in the days before computer modeling. Naval architects needed a way to draw a smooth curve through a set of points. The solution was to place metal weights (called knots) at the control points, and bend a thin metal or wooden beam (called spline) through the weights. The physics of the bending spline meant that the influence of each weight was greatest at the point of contact and decreased smoothly further along the spline. To get more control over a certain region of the spline, the draftsman simply added more weights.

The surface produced by splines always appears to be smooth and pleasantly looking. The reason for that effect is that while our eyes roll along a spline line, we subconsciously anticipate (following our genetically embedded sense of inertia) where the next point should be. When we indeed see it continue at the anticipated location, it creates in us a feeling of unconscious satisfaction and a sense of pleasant symmetry. As a matter of fact, what we were able to discover is that we consider the motion of the objects normal and almost unnoticeable if their behavior in our field of view follows some sort of a spline line. It appears that our visual anticipations are very much based on the same technique that the old craftsmen use to draw smooth lines.

Up to very recently, splines were an obscure tool that did not have much use outside of the draftsman’s’ toolbox. However, not too long ago, splines had an explosion of their usage thanks to the film industry. Before the 1990s, special effects in motion pictures and animations that change (or morph) one image into another through a seamless transition were achieved through cross-fading techniques on film. However, since the early 1990s, this has been replaced by computer software to create more realistic transitions. At the heart of this software were splines. Thanks to splines, a new era of computer animation has begun and truly amazing and realistic characters such as Shrek were born and entire studios created around these types of tools.

In today’s information age, splines have become one of the most popular tools to interpolate data. Mathematically, a metal or wooden spline could be modeled using a special function defined piecewise by third-degree polynomials. This function is called the “cubic spline interpolator” hence the degree of their polynomial functions. A Cubic Spline with a linear extension of its endpoint is called a “natural spline”.

In our research, we use natural cubic splines to perform the effective filtering of market signals through our proprietary and very unique analysis/visualization tool that we call “Spline Spectrums”.

9. Spline Spectrums

Many of the market parameters that carry very valuable information about market’s Sentiment and Perception, including the signals that we extract from the Order Book, are highly erratic, non-periodic processes. They may contain very abrupt moves as well as slow and smooth transitions between different time frames. In order to dissect those types of processes, a technique called “Spectrum Analysis” was invented at the beginning of the 19th century. The idea behind Spectrum Analysis is a separation of variables, which reduces problems expressed in two or more dimensions to a family of one-dimensional problems. This technique, for example, is the basis of tomography, a widely used tool of contemporary medicine. The best-known implementation of this method is The Fourier Transform - a mathematical operation with many applications in physics and engineering that expresses a mathematical function of time as a function of frequency, known as its Frequency Spectrum. For example, the transform of daylight could be presented as a mathematical representation of the magnitudes and phases of the individual colors that make it up. When we pass the daylight through a prism, we essentially utilize the Fourier transform to extract the rainbow of colors that form it. The most significant advantage of using algorithms and devices that are based on the Fourier Transform is their ability to visually represent relatively complex observations in a very compact and easy-to-comprehend format.

Consider the following. If we are listening to a choir that consists of many male and female singers, it is virtually impossible to detect the singers that have high-pitched voices and who sings in a much lower octave. Even if we recorded the sound of this choir and looked at it using an oscilloscope, we wouldn’t be able to discern the voices of individual singers from one another. However, if we passed this sound through a series of filters each tuned to a single specific frequency, the result would be drastically different. By measuring the signal strength of each filter, we could easily assess the relative impact of the voices with different pitches on the overall sound of the choir. Knowing the average “loudness” of a singer, we then can accurately estimate how many singers sing in any particular octave. More so, if we plot the filters’ output signals using a bar graph where each bar height corresponds to the signal strength of a particular frequency filter, we could create one of the most powerful visual signal analysis tools – Fourier Transform Spectrums. Although these spectrums are widely used in hundreds of engineering applications, they all have the same weakness. As it turns out, Fourier Transform Spectrums could only be efficiently used if the processes they analyze have a highly periodic character. In other words, they are only efficient if applied to signals like sound, mechanical vibrations, heartbeats, etc., that consist of periodical (sine wave-like) components. Unfortunately, most of the market information, including price fluctuations, Order Book bid/ask ratios, Volatility, etc., is not necessarily highly periodical. It, of course, limits the use of Fourier Transform Spectrums for efficient visualization of market signals.

Realizing this problem back in the late 90s, I came up with an idea to use natural cubic splines instead of Fourier filters in order to form new types of analytical tools that did not exist before – Spline Spectrums. At their heart is a set of splines that have different elasticity. Some of them are very easy to “bend” and some are very difficult. The easily bendable, flexible splines could “follow” the points in a data set very closely and “catch” even the slightest changes in the data flow. At the same time, the stiff, rigid splines only bend slightly at each data point, thus “ignoring” the most abrupt changes in the data set. The difference between endpoints of each spline could be plotted as a bar graph that represents a Spline Spectrum.

It turns out the Spline Spectrums are as powerful for market data analysis as Fourier filters for sounds and electromagnetic waves analysis. The perception they create significantly enhances our intuition about possible future changes in the market conditions. We have tested the Spline Spectrums with hundreds of traders in the past 12 years. The results of those experiments have conclusively proved their incredible efficiency for amplifying the traders’ intuition. Within only a few weeks of training and getting used to the spectrums, the majority of the test participants were able to improve their market sentiment reading skills and enhance their trading results.

10. Building the Intuition Amplifiers

Let us go back to the Order Book. It is obvious that all the information that is carried by the Order Book is very complex, highly dynamic, and incredibly stochastic. In order to effectively use the tools that we discussed earlier, we needed to extract a better initial signal without losing the accuracy of our measurements. Let’s consider the following logic that helped us in transforming the book’s information into a much more manageable format.

By observing and physically measuring the effect of bid/ask changes on the top of the book’s price fluctuations, it became apparent to us that:

• The further away from the top of the book a bid or ask order is, the less influence it has on the price changes observed at the top of the book.
• The larger the size of the order, the more influence this order has on future price fluctuations.
• The longer an order “sits” on the book without a fill or a cancellation, the less impact it has on the current price levels.

If we were to assign weights to each order on the book according to the points above, we then could create weighted sums of all the Bids and all the Asks that would represent their respective overall influence on the book’s behavior. Creating the ratio between the weighted sum of all the Bids and the weighted sum of all the Asks forms a signal that is much more manageable for its further analysis, filtering, and transformation; we call this signal “The Traders’ Sentiment”.

Applying the Spline Spectrums to the traders’ sentiment signal described above creates the Sentiment Spectrum – a one-of-a-kind, incredibly powerful, and efficient tool for Intuition Amplification.

Below is the description of some practical implementations of the Sentiment Spectrums and other Traders’ Sentiment based Indicators that we have developed over the past 12 – 14 years.

11. Stealth Sentiment Spectrum Gauge

This particular application uses natural cubic splines that have relative elasticity coefficients ranged between 3 and 58. The relative elasticity coefficient (expressed in percent) is the measure of accuracy with which a spline follows its knots. The most flexible spline used in this application had an elasticity of 3, and the most rigid one had an elasticity of 58. Altogether we used 55 different splines with their elasticity evenly spread between 3 and 58. These splines create the measure of the trading patterns that could be associated with the activities of different groups of traders that exhibit various frequencies of order placement on the book. We, of course, cannot physically identify those groups. However, the Sentiment Spectrum can adequately represent their behavioral patterns.

For example, active day traders place their orders more frequently than swing traders. Using this information to filter the overall trading activity registered in the Order Book creates a unique opportunity to see the intent of different groups of traders and to display this intent in the form of a very concise bar graph.

As we discussed earlier, In order to display the Traders’ Sentiment signal, we use the values produced by the Spline Spectrums and normalize them by the sliding time window (concept discussed in paragraph 6). These measurements are updated in real-time, creating the sliding time window that creates the reference points for the current sentiment levels. The results of these measurements are, in turn, displayed in the form of a histogram (called the Stealth Sentiment Spectrum Gauge).

In the gauge illustrated below, the value of the shortest activity filter (the sentiment measure of the most frequently trading group registered in the current time frame) is placed in the middle of the histogram. The values of longer filters are on the left and right of this central bar. This creates a graph where the sentiment of the most active traders is displayed in the center, and the sentiments of other less frequent traders are placed on its sides. The lower the trading frequency of a trading group filtered by the corresponding filter, the further this group is represented from the central bar. This type of ordered display makes the visual representation of the entire Stealth Sentiment Spectrum Gauge very intuitive to use.

12. Use of Colors

In the middle of the Stealth Sentiment Spectrum Gauge is the reference level (i.e., neutral baseline represented in the picture above by a dark-green horizontal line). If all of the bars in the Sentiment Spectrum are located above this reference level, then the overall sentiment exhibited by the traders of all the activity groups is bullish. The strongest bullish sentiment, for example, is presented by the spectrum where all the bars form an almost perfect triangle pointed upwards. The opposite is true for the bearish sentiment.

The color represents the rate of change of the sentiment compared to its previous levels over one Sentiment Compression Interval.

There are two distinct color palettes used in the Sentiment Spectrum:

• The blue or bullish palette that consists of colors ranging from dark purple, dark blue to very light blue, almost bluish-white colors.
• The red or bearish palette that consists of colors ranging from dark purple, dark red colors up to orange, bright yellow, and almost yellowish-white colors.

The brighter the color, the greater is the acceleration of the traders’ intent towards either bullish or bearish sentiment. This unique way of presenting the picture of the real-time sentiment enables a trader to anticipate the change in buying or selling activities prior to any actual price movements.

There is an infinite variety of shape and color combinations that a trader can experience by observing the Stealth Sentiment Spectrum Gauge. However, in our 12 years of experimenting with the Sentiment Spectrums, we consistently observed that by associating their shapes and colors with the following price moves, an average-skilled trader can develop very accurate anticipation skills in 2–3 weeks of self-training. We have also proved that the shapes and colors of the Sentiment Spectrums do not depend on the actual security. They are universal and indicate the bullish or bearish sentiment the same way for all securities.

The following is a typical interpretation of the market conditions depicted by the shown above Stealth Sentiment Spectrum Gauge.

As you can see, the central part of the sentiment Spectrum is below the horizontal reference line and is pointing downwards. The colors of the graph are mostly red with a very bright shade of orange and yellow right in the middle of the spectrum. The outside bars of this histogram are still above the reference line and they present in a dark shade of purple.

This Sentiment Spectrum could mean that the current sentiment of the traders is changing from being recently mildly bullish to a pronounced bearish sentiment. Although some infrequent groups of traders (the outside wings of this graph) are still somewhat bullish (the bars that represent their sentiment are still above the reference line), their sentiment is not increasing towards further buying (the color of their bars is purple, which is neutral). At the same time, the more frequent traders (scalpers, day traders, swing traders, etc.) are bearish with an increased intensity in their Sell orders. This is indicated by the bright orange and yellow middle bars below the reference line.

As indicated in the aforementioned, the Sentiment Spectrum is capable of generating an endless number of colors and shapes that could be very reliably associated (by experienced users) with many different market conditions. For example, if the Sentiment Spectrum is at its peak, it indicates extreme bullish or bearish activity when the traders’ sentiment cannot get any more bearish or any more bullish (i.e., the sentiment exhaustion point). This creates a sentiment reversal possibility.

The example of this type of situation is illustrated below when the bullish sentiment of the S&P 500 index e-mini futures traders reached the exhaustion point (indicated by the red dot on top of the spectrum), signaling a possible pullback in their buying activity.

Our experimental work with Sentiment Spectrums has shown us that it is important to spend considerable time observing their behavior. The key to developing reliable anticipation skills (intuition) is the ability to create stable associations between the images the spectrums are generating and the price moves that occur as a result of the changes in the market sentiment registered and displayed by the Sentiment Spectrums. The more time spent observing the behavior of the Sentiment Spectrums, the more accurate trading decisions could be made.

13. Traders’ Commitment Gauge

It is a well-known psychological phenomenon that the majority of traders make their buy decisions when they believe that the price has fallen too far, too fast. Conversely, they tend to sell a security if its price has risen too far, too fast. If this situation occurs, it usually manifests itself through the increased number of order cancellations on either the Bid Side or the Ask Side of the Order Book. By measuring the relative cancellation frequency of buy and sell orders, it is possible to extract information about traders’ intentions to buy or sell a security. Again, by using the Sliding Time Window concept applied to the different uncorrelated time frames, we were able to construct an algorithmic procedure to register and measure this valuable aspect of traders’ sentiment. We call it “The Trader’s Commitment”. This relative cancellation frequency is measured by a one-dimensional linear scale, and the visual representation of the Traders’ Commitment could be done by using a gauge-like linear indicator. The picture below illustrates one of our practical implementations of this gauge.

There are two clearly marked levels on this gauge that are +80% and –80%. These levels represent situations when the overwhelming majority of traders (over 80%) are committed to sell or buy the security.

If the gauge displays a positive number in its top section, then the cancellation activity on the Bid side of the book is higher (by the displayed percentage) than the cancellation activity on the Ask side of the book.

If this happens, it could mean that the traders’ commitment to “stick” to their Sell orders is greater than to their Buy orders (i.e., possible anticipation of an upcoming price decline). If there is a higher number of cancellations that have been registered on the Ask side of the book (the percentage number appears on the bottom of the commitment gauge in red), this could represent a possible price increase. The greater the percentage indicated by the gauge, the greater the probability for the price to move in the direction of the exhibited traders’ commitment.

In order to assess the efficiency of this Intuition amplification gauge, we have conducted hundreds of trials involving intraday traders. Overall, by observing this gauge for two to three weeks, an average trader was able to increase his/her ability to anticipate upcoming price moves by 20 to 30%.

14. Trading Equilibrium Gauge

Based on the assumption that all of the processed orders on the Order Book should result in the price movement that fairly represents those filled orders (i.e., the market efficiency assumption), there is a way to calculate the difference between the current actual price level and its fair value. This gives a trader the insight into how far the current situation observed on the Order Book is from its efficiency state. This information could enable the trader to make more accurate trading decisions and better anticipate the timing of exploitable market’s inefficiencies. Those inefficiencies are measured and displayed in the form of price deviations from their efficient levels. One of the implementations of this Intuition Amplification Gauges is shown below.

The left side of the gauge contains calculated price levels ranging from the equilibrium level up to the +4 standard deviation level and down to the –4 standard deviation level.

There is a price scale to the right of the price deviation levels with two markers (yellow and cyan colors). These markers indicate the highest and the lowest levels of the price registered over the current sliding time window.

They help a trader to assess the current price volatility levels in terms of standard deviations.

The yellow marker indicates the highest price registered and the cyan-colored marker indicates the lowest price registered during the current sliding time window.

In the middle of the gauge is a white arrow that displays the most recent (i.e., last) traded price of the analyzed security. This arrow’s position points to where the current price is in terms of standard deviations relative to the price equilibrium level. This information helps traders to understand how much the markets are “overbought” or “oversold,” which gives them additional information to improve their trading intuition and anticipation skills.

On the right side of the gauge is the BIAS gauge that consists of two indicators:

• A vertical bar that changes color.
• A small green marker that slides over a vertical price scale.

The small green marker indicates how far the current price is from the expected level of the equilibrium price in the next sliding time window. This information is very valuable as it allows the trader to anticipate the change in the market’s efficiency over the next frame of the sliding time window.

The BIAS gauge deals with the general direction of the equilibrium price. If the equilibrium price is increasing compared to the last Sliding Time Window, the BIAS is bullish. Conversely, if the equilibrium price is lower in the new time window, the BIAS is bearish.

Overall, the Trading Equilibrium Gauge is another effective tool developed by our company to amplify the intuition of traders. It has also been tested in real-time and in live market conditions by a variety of traders. The results of those experiments have objectively established a significant increase in the traders’ abilities to anticipate short-term changes in market conditions.

Below is a snapshot of one of our cockpit-like trader decision support platforms - Stealth Trader that features the spectrums and gauges described above. We, of course, have developed many different intuition amplifiers (some of them are shown in the picture below as well) and continue actively in our research and development efforts building solutions for institutional and commercial users. For the purpose of this paper, our focus has been the main types of Intuition Amplifiers discussed above.

15. Conclusion

The sole purpose of this paper was to demonstrate a Mathematical Psychology-based approach to enhancing the traders’ intuition used in their day-to-day decision-making processes. Many of the concepts discussed herein are the results of our original research that stemmed from our belief that a person’s intuition, anticipation skills, and the ability to develop stable and virtually instantaneous associative reactions to rapidly changing market conditions could be dramatically improved by using a variety of visualization and hidden patterns extraction tools powered by the real-time data stream from electronic Order Books. As a result of our research, many cockpit-like trading decision-making platforms were designed, built, and implemented in different live trading environments and constructs. We are convinced that this area of Artificial Intelligence research could be extremely fruitful and lead to the development of brand-new, non-traditional trading tools to bring the reliability of trading decisions to a much higher level.

We welcome any interest in our arsenal of Intuition Amplifiers and will be glad to set up practical, hands-on trials of our tools.